Question

120 ​-inch length of ribbon is to be cut into three pieces. The longest piece is to be 40 inches longer than the shortest​ piece, and the third piece is to be half the length of the longest piece. Find the length of each piece of ribbon.

Answer 1

1. Let
Shortest piece = x
Longest piece = y
Third piece = z

2.
Shortest piece = x
Longest piece = 40 + x
Third piece = (40 + x)/2 OR 20 + 0.5x

3. Add all the expressions since you know that the total of all the pieces is 120 inches
40 + x + 20 + 0.5x + x = 120.

4. Add the whole numbers first, then add the variables.
40+20=60
x+0.5=2.5x
60+2.5x=120

5. To get rid of the 60, do the opposite of addition which is subtraction and subtract 60 from both sides.
2.5x=120-60
2.5x=60

6. Do the same but rather than addition, do the opposite of multiplying which is dividing, on both sides.
x=60/2.5
x=24

7.
Shortest piece = 64-40=24 inches
Longest piece = 24+40=64
Third piece = 64/2=32